Question

Two substances A and B have specific heats c and 2 c respectively. If A and B are given Q and 4Q amounts of heat respectively, the change in their temperatures is the same. If the mass of A is m, what is the mass of B?

Answer 1

Let the mass of B = M.

Let the change in temperature be T for both the bodies, A and B.

The amount of heat in a body is given as 

Q = m × c × Δ T

For body A,

Q = m × c × T 

`=> "T" = "Q"/("mc")`    ...(i)

For body B,

4Q = M × 2c × T 

`=> "M" = (4"Q")/(2"c" xx "T")`

From (i), T = `Q/(mc)`

`=> "M" = (4Q)/(2c xx Q/(mc)) = 2m`